Twitter, which is said to be entertaining buyout bids, may also have Microsoft as a potential suitor, a source told CNBC on Monday.

CNBC's David Faber reported on "Closing Bell" that the social media giant is moving closer to a formal sale process for the company, according to sources familiar with the situation. However, he said, that does not mean it is in that formal process yet.

According to sources familiar with the matter, Facebook is unlikely to have interest in buying the social network. Moves toward a possible sale are expected to accelerate in the coming days, sources tell CNBC, with a deal potentially happening within the next 30-45 days.

On Monday, a report in Bloomberg said Walt Disney was also among those interested in Twitter.